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The first ever real bistable memristors – Part I: theoretical insights on local fading memory
No full textIt has been recently shown that a current-controlled
extended memristor may exhibit bistable steady-state behavior
under dc as well as ac periodic stimuli. This brief employs standard
techniques from the nonlinear dynamics theory as well as
circuit and system theoretic concepts to explain the origin of the
asymptotic bistable behavior, which is the signature of a local
fading memory capability. Part II derives the first real memristor
featuring similar complex dynamics
The First Ever Real Bistable Memristors - Part II: Design and Analysis of a Local Fading Memory System
No full textPart I has provided theoretical insights on the
concept of local fading memory and analyzed a purely mathematical
memristor model that, under dc and ac periodic stimuli,
experiences memory loss in each of the basins of attraction of two
locally stable state-space attractors. This brief designs the first
ever real memristor with bistable stationary dc and ac behavior. A
rigorous theoretical analysis unveils the key mechanisms behind
the emergence of nonunique asymptotic dynamics in this novel
electronic circuit, falling into the class of extended memristors
Theoretical Foundations of Memristor Cellular Nonlinear Networks: Memcomputing With Bistable-Like Memristors
No full textThis paper presents the theory of a novel memcomputing
paradigm based upon a memristive version of standard
Cellular Nonlinear Networks. The insertion of a nonvolatile
memristor in the circuit of each cell endows the dynamic array
with the capability to store and retrieve data into and from
the resistance switching memories, obviating the current need
for extra memory blocks. Choosing the parameters of each
cell circuit so that the memristors may undergo solely sharp
transitions between two states, each processing element may be
approximately described at any time as one of two first-order
systems. Under this assumption, the classical Dynamic Route
Map may be employed to synthesise and analyse the data storage
and retrieval genes. A new system-theoretic methodology, called
Second-Order Dynamic Route Map, is also introduced for the first
time in this paper. This technique allows to study the operating
principles of arrays with second-order processing elements, as is
the case, in the proposed network, if the set up of cell circuit
parameters induces analogue memristive dynamics. This paper
shows how the novel tool may be adopted to investigate the
operating mechanisms of a cellular array with second-order cells,
which compute the element-wise logical OR between two binary
images
Theoretical Foundations of Memristor Cellular Nonlinear Networks: A DRM2-Based Method to Design Memcomputers With Dynamic Memristors
No full textIn the memristive version of a standard spaceinvariant
Cellular Nonlinear Network, each cell accommodates
one first-order non-volatile memristor in parallel with a capacitor.
In case, the resistance switching memory may only undergo
almost-instantaneous switching transitions between two possible
resistive states, acting at any time, as either the on or
the off resistor, the processing elements effectively operate as
first-order dynamical systems, and the classical Dynamic Route
Map technique may be applied to investigate their operating
principles. On the contrary, in case the memristors experience
smooth conductance changes, as the bioinspired array implements
memcomputing paradigms, each cell truly behaves as
a second-order dynamical system. The recent extension of the
Dynamic Route Map analysis tool to systems with two degrees
of freedom constitutes a powerful technique to investigate the
nonlinear dynamics of memristive cellular networks in these
scenarios. This paper exploits this system-theoretic technique,
called Second-Order Dynamic Route Map, to introduce a novel
systematic procedure to design memristive arrays, in which a
given memcomputing task is executed by ensuring that, depending
upon the network inputs and initial conditions, the analogue
dynamic routes of the states of the processing elements, namely
capacitor voltages and memristor states, asymptotically converge
toward pre-defined stable equilibria
Mem-computing CNNs with bistable-like memristors
No full textIn this paper we propose a new mem-computing image
processing architecture, called Memristor Cellular Nonlinear
Network, which leverages the unique capability of nonvolatile
memristors to compute and store data in the same physical
nano-scale locations. Adopting a bistable-like memristor in place
for the linear resistor in the standard realization of a cell of
the nonlinear dynamic array, the resulting network is capable
to process information by exploiting the time evolution of the
voltages across the memristors as well as to store/retrieve results
into/ from the memristances. This attractive feature, absent in a
standard Cellular Nonlinear Network, may pave the way towards
the future development of a new generation of visual processors
with unprecedented spatial resolution
Image Mem-Processing Bio-Inspired Cellular Arrays with Bistable and Analogue Dynamic Memristors
No full textBy introducing memristors into circuit design, the
limitations of traditional purely-CMOS hardware may be overcome.
However, an extension of standard techniques for the
analysis and design of conventional computing structures may
be necessary to allow their applicability to the memristive
counterparts. This paper adopts a generalization of the Dynamic
Route Map system-theoretic concept to elucidate the mechanisms
by which bio-inspired arrays of locally-coupled circuits, employing
memristors with either bistable-like or analogue dynamic
switching behaviours, accomplish image mem-processing tasks
through the dynamical evolution of their states toward predefined
equilibria
DC behaviour of a non-volatile memristor: part II
No full textAdopting the system theoretic tools introduced in
part I, this paper gains a deep insight into the fading memory
effects emerging in a non-volatile memristor under DC inputs.
Experimental evidence for the history erase phenomenon is also
provided here
Theory of CNNs with hafnium oxide RRAMs
No full textThe unique combined capability of memristor nanodevices
to process signals and store data in the same physical
volume may resolve the performance bottleneck of current
purely-CMOS visual microprocessors, in which only a limited
number of computing structures, known as Cellular Nonlinear
Networks, may be integrated on top of image sensor arrays. The
reason behind the poor spatial resolution of these smart sensors
lies in the large integrated circuit area used up by each
processing element in the multivariate signal processing cellular
networks, mainly due to the need to endow them with data
storage functionality, with obvious advantages in terms of
computing speed. Memristor technologies may resolve this
performance bottleneck since they are able to combine both
signal processing and data storage capabilities within a nanoscale
volume. As a result, their use in novel CNN hardware
implementations may obviate the need for apposite memory
blocks within each processing element. Furthermore, the peculiar
nonlinear dynamics of memristors may be harnessed to extend or
enhance the signal processing functionalities of CNNs. In this
work we establish the theoretical foundations of a diffusivelycoupled
Memristor CNN in which the linear resistor appearing
in the standard CNN cell implementation is replaced by a
hafnium oxide resistive random access memory device, including
a series transistor limiting the current flowing through the
memristor during on switching. Adopting an accurate physicsbased
model for the hafnium oxide resistance switching memory,
a thorough theoretical investigation of the Dynamic Route Map
of the memristor CNN cell allows to gain a deep understanding of
the working principles of the novel nonlinear dynamic array.
Numerical simulations covering a large number of image
processing operations validate the theoretical developments, and
reveal the add-on functionalities memristors endow the proposed
network with, including the fascinating possibility to store and
retrieve data, an impossible task for standard implementations
Edge of Chaos Theory Resolves Smale Paradox
No full textNo isolated system may ever support complexity.
Emergent phenomena may however appear in an open system,
if, as established by the Edge of Chaos theory, some of its constitutive
elements feature the capability to amplify infinitesimal fluctuations
in energy, provided an external source supplies them with a
sufficient amount of DC power, which is known to be a signature
for locally-active behaviour. In particular, complex behaviours,
including static and dynamic pattern formation, may emerge in
arrays of identical diffusively-coupled cells, if and only if the basic
unit is poised on a particular sub-domain of the Local Activity
regime, referred to as Edge of Chaos, within which a quiet state
hides in fact a high degree of excitability. Here we show, for the
first time, that these counterintuitive phenomena may emerge
in a basic memristor cellular neural network, consisting of two
identical diffusively-coupled second-order cells. The proposed
bio-inspired array represents the simplest ever-reported open
system, which reproduces the shocking phenomenon, reported
by Smale in 1974, when, while studying a model from cellular
biology, he observed two identical reaction cells, “mathematically
dead” on their own, pulsating together upon diffusive coupling.
Impressively, the bio-inspired two-cell reaction-diffusion network
contains only nine circuit elements, specifically two DC voltage
sources, three linear resistors, two linear capacitors, and two
functional niobium oxide (NbO) memristors from NaMLab.
Applying the theory of Local Activity to an accurate model of the
memristor oscillator, a comprehensive picture for its local and
global dynamics may be drawn, providing a systematic method
to tune the design parameters of the two-cell array to enable
diffusion-driven instabilities therein
Fading memory effects in a memristor for Cellular Nanoscale Network applications
No full textCNN based analogic cellular computing is a unified
paradigm for universal spatio-temporal computation with
several applications in a large number of different fields of
research. By endowing CNN with local memory, control, and
communication circuitry, many different hardware architectures
with stored programmability, showing an enormous computing
power - trillion of operations per second may be executed on a
single chip -, have been realized. The complex spatio-temporal
dynamics emerging in certain CNN may lead to the development
of more efficient information processing methods as compared
to conventional strategies. Memristors exhibit a rich variety of
nonlinear behaviours, occupy a negligible amount of integrated
circuit area, consume very little power, are suited to a massivelyparallel
data flow, and may combine data storage with signal
processing. As a result, the use of memristors in future CNNbased
computing structures may improve and/or extend the
functionalities of state-of-the art hardware architectures. This
contribution provides a detailed analysis of the system-theoretic
model of a tantalum oxide memristor, in view of its potential
adoption for the implementation of synaptic operators in CNN
architectures
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